Problem: Calculate the product below and give your answer in scientific notation. $ {\left(2.0\times 10^{0} \right) \times \left(6.0\times 10^{5} \right) =\ ?} $
Explanation: Start by collecting the significands and exponents. $ ({2.0} \times {10^{0}}) \times ({6.0} \times {10^{5}}) = ({2.0} \times {6.0}) \times ({10^{0}} \times {10^{5}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {12.0} \times {10^{0 \,+\, 5}}$ $= {12.0} \times {10^{5}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${12.0}$ is the same as ${1.20 \times 10}$ or ${1.20 \times 10^{1}}$. $ = {1.20 \times 10^{1}} \times {10^{5}} $ $ = 1.20 \times 10^{{1} + {5}} $ $= 1.20\times 10^{6}$